lower bound: | 144 |
upper bound: | 149 |
Construction of a linear code [204,7,144] over GF(4): [1]: [204, 7, 144] Linear Code over GF(2^2) Code found by Axel Kohnert Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 0, 1, 1, w^2, w, w^2, w^2, 0, 0, w^2, w^2, 0, 0, 1, 1, 1, w^2, w, w, 1, 1, 0, 0, 0, 1, 1, 1, w, 0, w^2, w^2, 0, 0, 1, 0, w^2, 1, 0, 0, 1, w^2, w, 0, w^2, 0, w, w, 1, 0, w, w, w, w^2, w, 1, w^2, 1, 1, w^2, 1, w, w, w^2, 0, 1, w^2, 1, 0, w, 0, 0, w, w^2, w, w, w^2, 1, w^2, 1, w^2, w, 1, w, w, 0, w, w, w^2, w^2, w, w^2, 1, 0, 0, 0, 0, 1, 1, 0, 1, w^2, 1, w, w^2, w, 1, 1, w^2, w, 0, 0, w, w^2, 0, w, 0, w, 0, w^2, 0, 1, 0, w, w^2, w^2, w, w^2, w^2, 1, 1, 0, 0, 0, w^2, w, 1, w^2, 1, 0, 1, 0, w, 0, w, 1, w, 1, 1, w^2, w^2, w^2, w, 0, w, 0, w, 1, 1, w, 0, 1, 1, 0, w^2, 0, 1, w, 0, 0, w, 1, w, 0, 1, w^2, 0, w^2, 1, 1, 1, 0, 1, 0, w, 1, w, 1, 0, w^2, 1, 1, 1, 1, w, 1, w, w^2, 1 ] [ 0, 1, 0, 0, 0, 1, 0, w^2, w, w, 0, w^2, w, 0, 1, w, 1, 0, w^2, w^2, 1, w^2, 1, 0, w, w, w^2, 0, w, 1, 0, 0, 0, 1, w, w^2, w, 1, 1, 1, 0, 1, w^2, 0, w^2, w^2, w, w, 1, w^2, 0, w, w, w, 0, w^2, 1, w, w^2, 0, w, 1, w, w^2, 1, 0, 1, 0, w^2, 0, w^2, 0, w, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, w^2, w^2, w^2, w, w, w, 0, 0, w^2, w^2, 1, 1, 1, w, w^2, w^2, w, 0, 1, w^2, w^2, w, 1, w^2, w, 0, w^2, 1, w, w, 1, w, 1, 0, 1, 1, w, w, 1, 1, w, 1, 0, 0, 0, w, 1, 1, w^2, w^2, 1, w, w, w^2, w^2, w^2, w, w, 0, 1, w^2, w^2, w, 0, w, 1, 1, w^2, 1, w, w, 1, w^2, 0, 1, 0, w^2, 1, w^2, 0, w^2, w^2, w, w^2, 1, 1, w, 0, w^2, w^2, w, 1, w^2, 1, w, w^2, w^2, 0, 0, 0, w, 0, w, 0, 1, w^2, 1, 0, 1, w^2, w, 1, w, w, w, w^2, w, w^2, w, 1 ] [ 0, 0, 1, 0, 0, w^2, 0, w^2, 1, w^2, 1, w, w^2, 1, w, w^2, w^2, 0, w^2, 0, 0, 1, 0, w^2, w^2, w^2, 0, w, 1, 1, 1, w, 1, w, w^2, w^2, 0, 0, 1, 0, w^2, 0, 1, 1, 0, w^2, 1, w, w^2, w^2, 0, 1, 1, w, 1, 1, 1, w^2, 1, w^2, 1, 1, w^2, 1, 1, w, 1, 0, 1, 0, 0, w^2, w^2, 1, 0, w, 1, w^2, 0, w, 0, 0, w^2, 0, 0, w^2, 1, 0, 1, 0, 1, 0, 1, w^2, w, 0, w, w, w, 0, 0, w, w^2, 1, w^2, 0, w, 1, 1, 1, 1, w, w^2, w, w^2, 0, 0, 1, w^2, 1, w, 1, 1, w, w, w^2, 1, w, 0, w^2, 1, 0, w^2, w^2, w, 1, w, 1, w^2, w^2, 0, 1, 0, 1, 1, w, 0, 0, w^2, 1, 0, w^2, w, 0, w, 0, w^2, 1, 0, w^2, w, 1, 1, 1, 0, 0, 0, 1, 0, w^2, 0, w^2, 0, w^2, w, 1, 0, 0, 0, 0, w, 0, 1, w^2, 0, w, w^2, w^2, w, w^2, w^2, w, w, 0, w, 1, w, w, w, w^2, 0, 1, w^2, 0 ] [ 0, 0, 0, 1, 0, w^2, 0, w^2, 0, w^2, w^2, 0, 0, w, w^2, 0, w, 0, 1, 0, w^2, 1, 0, w, 0, 0, 0, w^2, w, w^2, 1, w^2, w^2, 1, 1, 0, w^2, 1, 1, w^2, 0, 1, w^2, 0, 1, 0, 1, w^2, 1, w, w, w^2, 0, 1, 1, w^2, w^2, w^2, w^2, w, 1, 1, w^2, w, w, w^2, 0, w^2, 0, w, 1, w, 1, 1, w, w^2, 0, w^2, w^2, w^2, 0, 0, w, 1, w^2, 1, w^2, w^2, w, 1, w^2, w, w^2, w^2, 0, w^2, w^2, w, 1, 1, w^2, w^2, 0, w, 1, w^2, 1, w^2, 0, 1, 0, 1, w^2, 1, 1, w, w, w, 1, w, w, 0, w, 1, w, w, w^2, 1, w, w, w^2, 1, w, 1, 0, 1, w^2, w, w, w^2, 0, w, w, w, w, 1, 1, 1, w^2, 1, w^2, w, 1, 0, 0, 0, w, 0, w^2, 0, w^2, w, w^2, w, 1, w, 0, w, w, 1, w^2, w, 1, w^2, 0, 0, w, w^2, 1, w, 1, w^2, w^2, w^2, w, w^2, 1, w, 1, w, w, 1, w^2, w, w, 0, w^2, w^2, w^2, w, w^2, 0, w^2, 1 ] [ 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, w^2, 1, w^2, 0, w, 0, w^2, 0, 1, w^2, 1, 1, w^2, w, 0, 0, w, w^2, 0, 0, 1, w^2, w^2, 1, 0, w^2, w^2, 0, w^2, w, w, 1, w, 1, w, 1, w, w^2, 0, w, 1, w^2, w, w^2, 1, w, w, w, w, 0, 0, w, w, 0, w, w^2, 0, 1, w, 0, w, 1, w, w^2, 0, w^2, w, w, 1, 1, w^2, w^2, w^2, w, 1, w^2, 1, 1, 1, w^2, 0, 1, w, w^2, 0, 1, w^2, 1, w^2, w, w^2, w, 0, 0, 0, 1, 0, w^2, 0, w^2, w^2, w^2, w, w^2, w, w^2, 0, w, 0, 0, w, w^2, 1, 0, 1, w, 1, w, 0, w^2, w^2, 1, 1, w^2, 1, w^2, w^2, 0, 0, w, w, 1, w^2, w^2, w, w, 0, w, 0, w, 0, w, w^2, w^2, 1, 0, w, 0, 1, 0, 1, w, 0, w^2, w^2, 1, 0, w, w^2, 1, w, 1, w, w^2, 1, w^2, w, w, w, 0, 1, w, 0, w^2, 1, 1, w, 0, w, 1, w^2, w, w, w, w, 1, w^2, 1, w^2, w ] [ 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, w, w, w, w^2, w^2, w^2, w^2, 0, 0, 0, 0, 0, 1, w, w, w, w^2, w^2, w^2, 0, 0, 0, 0, 1, 1, w, w, w, w, w, w, w^2, w^2, 0, 0, 1, 1, w^2, w^2, w^2, w^2, 0, 0, 0, 0, 0, 1, w, w, w, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, 0, 0, 1, 1, 1, 1, 1, w, w, w, w^2, w^2, w^2, 0, 0, 0, 1, 1, 1, w, w, w^2, w^2, w^2, w^2, 0, 0, 1, 1, 1, w, w, w, w, w^2, w^2, w^2, 0, 1, w, w, w, w^2, w^2, w^2, 0, 0, 1, 1, 1, 1, 1, w, w, w, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, 0, 0, 0, 0, 1, 1, 1, w, w, w, w^2, 1, 1, w, w, w, w, w, w^2, w^2, w^2, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, w, w, w, w, w^2, 0, 0, 0, 1, w, w^2, w^2, w^2, w^2, w^2, 0, 0, 0, 1, 1, w, w, w^2, w^2, w^2, 0, w^2, w^2, 0, 0, w, w, w, w, w, 0, 1, 1, 1, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1 ] where w:=Root(x^2 + x + 1)[1,1]; last modified: 2006-09-20
Lb(204,7) = 144 Koh Ub(204,7) = 149 follows by a one-step Griesmer bound from: Ub(54,6) = 37 follows by a one-step Griesmer bound from: Ub(16,5) = 9 follows by a one-step Griesmer bound from: Ub(6,4) = 2 is found by construction B: [consider deleting the (at most) 4 coordinates of a word in the dual]
Notes
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